DC calculus View Full Text


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Article Info

DATE

2018-04

AUTHORS

Luigi Ambrosio, Jérôme Bertrand

ABSTRACT

In this paper, we extend the DC calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a Radon measure respectively. We show that these objects share various properties with their analogues on smooth Riemannian manifolds. More... »

PAGES

1037-1080

References to SciGraph publications

  • 2014. Logarithmic Sobolev Inequalities in ANALYSIS AND GEOMETRY OF MARKOV DIFFUSION OPERATORS
  • 2001-10. Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces in MATHEMATISCHE ZEITSCHRIFT
  • 2004. Riemannian Geometry in NONE
  • 1987. Riemannian Geometry in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00209-017-1926-8

    DOI

    http://dx.doi.org/10.1007/s00209-017-1926-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092125343


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